We present a Bayesian approach to the problem of inferring the number of inversions and translocations separating two species. The main reason for developing this method is that it will allow us to test hypotheses about the underlying mechanisms, such as the distribution of inversion track lengths or rate constancy among lineages. Here, we apply these methods to comparative maps of eggplant and tomato, human and cat, and human and cattle with 170, 269, and 422 markers, respectively. In the first case the most likely number of events is larger than the parsimony value. In the last two cases the parsimony solutions have very small probability.